In this paper, we propose a projection dynamical system for solving the split equality problem, or more generally the approximate split equality problem, in Hilbert spaces. The proposed dynamical system endows with the continuous behavior with time for Moudafi’s alternating CQ-algorithm and Byrne and Moudafi’s extended CQ-algorithm. Under mild conditions, we prove that the trajectory of the dynamical system converges weakly to a solution of the approximate split equality problem as time variable t goes to \(+\infty \). We further derive the exponential-type convergence provided that a bounded linear regularity property holds for the approximate split equality problem. Several numerical examples are given to demonstrate the validity and transient behavior of the proposed method.

在本文中，我们提出了一种投影动力学系统，用于解决希尔伯特空间中的分裂等式问题，或更普遍的是近似分裂等式问题。对于Moudafi的交替CQ算法以及Byrne和Moudafi的扩展CQ算法，所提出的动力学系统具有随时间的连续行为。在温和条件下，我们证明了随着时间变量t变为\（+ \ infty \），动力学系统的轨迹弱收敛到近似分裂等式问题的解。如果有界线性正则性对于近似分裂等式问题成立，我们进一步推导指数型收敛。给出了几个数值例子，说明了该方法的有效性和瞬态行为。